(-4x-5)(6x-4)=0

Solution for (-4x-5)(6x-4)=0 equation:

(-4x-5)(6x-4)=0

We multiply parentheses ..

(-24x^2+16x-30x+20)=0

We get rid of parentheses

-24x^2+16x-30x+20=0

We add all the numbers together, and all the variables

-24x^2-14x+20=0

a = -24; b = -14; c = +20;
Δ = b2-4ac
Δ = -142-4·(-24)·20
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-46}{2*-24}=\frac{-32}{-48}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+46}{2*-24}=\frac{60}{-48}
=-1+1/4
$